Lp Solutions of -Backward Stochastic Differential Equations with Continuous Coefficients

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Abstract. In this paper, we study -backward stochastic differential equations with continuous coefficients. We give existence and uniqueness results for G-backward stochastic differential equations, when the generator is uniformly continuous in , and the terminal value with . We consider the G-backward stochastic differential equations driven by a G-Brownian motion in the following form: (1) where and are unknown and the random function , called the generator, and the random variable , called terminal value, are given. Our main result of this paper is the existence and uniqueness of a solution for (1) in the G-framework.